Residualized Factor

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224

/** D17 reference algorithms. JSON boundary validation is deliberate and shared.
 * Arrays are copied before sorting; callers' inputs are never mutated.
 * QR solves least squares without forming normal equations.
 */
type Data = Record<string, any>;
type Result = Record<string, any>;
class ContractError extends Error {
}
const fail = (code: string): never => { throw new ContractError(code); };
const num = (x: unknown): number => typeof x === 'number' && Number.isFinite(x) ? x : fail('INVALID_NUMBER');
function integer(x: unknown, lo: number, hi: number): number { const v = num(x); return Number.isInteger(v) && v >= lo && v <= hi ? v : fail('INVALID_PARAMETER'); }
function vec(x: unknown, min = 1): number[] { if (!Array.isArray(x))
    fail('INVALID_SHAPE'); const a = x as unknown[]; if (a.length < min)
    fail('INSUFFICIENT_DATA'); return a.map(num); }
function mat(x: unknown, min = 1): number[][] { if (!Array.isArray(x) || x.length < min)
    fail('INSUFFICIENT_DATA'); const a = (x as unknown[]).map(v => vec(v)); if (new Set(a.map(r => r.length)).size !== 1)
    fail('LENGTH_MISMATCH'); return a; }
function same(...x: {
    length: number;
}[]): void { if (new Set(x.map(a => a.length)).size !== 1)
    fail('LENGTH_MISMATCH'); }
function ids(d: Data, n: number): string[] { required(d, ['ids']); if (!Array.isArray(d.ids) || d.ids.length !== n)
    fail('LENGTH_MISMATCH'); if (d.ids.some((v: unknown) => typeof v !== 'string' || !/^[A-Za-z0-9_.-]+$/.test(v)))
    fail('INVALID_ID'); if (new Set(d.ids).size !== n)
    fail('DUPLICATE_ID'); return [...d.ids]; }
function required(d: Data, keys: string[]): void { for (const key of keys)
    if (!Object.hasOwn(d, key))
        fail('MISSING_FIELD'); }
function validDate(v: unknown): boolean { if (typeof v !== 'string' || !/^\d{4}-\d{2}-\d{2}$/.test(v) || v.startsWith('0000'))
    return false; const date = new Date(v + 'T00:00:00Z'); return Number.isFinite(date.valueOf()) && date.toISOString().slice(0, 10) === v; }
function context(d: Data, op: string): void {
    const keys = ['as_of', 'formation_at', 'inputs_available_at'];
    const evaluation = ['ic', 'rank_ic', 'spread', 'decay'].includes(op);
    if (evaluation)
        keys.push('outcomes_start_at', 'outcomes_end_at', 'outcomes_available_at');
    required(d, keys);
    if (keys.some(k => !validDate(d[k])))
        fail('INVALID_DATE');
    if (d.formation_at > d.as_of || d.inputs_available_at > d.formation_at)
        fail('FUTURE_INPUT');
    if (evaluation) {
        if (d.outcomes_start_at < d.formation_at || d.outcomes_end_at < d.outcomes_start_at)
            fail('INVALID_OUTCOME_WINDOW');
        if (d.outcomes_available_at < d.outcomes_end_at)
            fail('INVALID_DATE_ORDER');
        if (d.outcomes_available_at > d.as_of)
            fail('IMMATURE_OUTCOME');
    }
}
const sum = (a: number[]): number => a.reduce((s, v) => s + v, 0);
const mean = (a: number[]): number => sum(a) / a.length;
const dot = (a: number[], b: number[]): number => sum(a.map((v, i) => v * b[i]));
const tr = (a: number[][]): number[][] => a[0].map((_, j) => a.map(r => r[j]));
const mm = (a: number[][], b: number[][]): number[][] => { const cols = tr(b); return a.map(row => cols.map(col => dot(row, col))); };
function sd(x: number[], ddof = 0): number { const m = mean(x); return Math.sqrt(sum(x.map(v => (v - m) ** 2)) / (x.length - ddof)); }
function standard(x: number[]): number[] { const m = mean(x), s = sd(x); if (s <= 1e-14 * Math.max(1, ...x.map(Math.abs)))
    fail('CONSTANT_CROSS_SECTION'); return x.map(v => (v - m) / s); }
function corr(x: number[], y: number[]): number | null { same(x, y); if (Math.max(...x) === Math.min(...x) || Math.max(...y) === Math.min(...y))
    return null; const xm = mean(x), ym = mean(y), a = x.map(v => v - xm), b = y.map(v => v - ym), den = Math.sqrt(dot(a, a) * dot(b, b)); return den <= 0 ? null : Math.max(-1, Math.min(1, dot(a, b) / den)); }
function ranks(x: number[]): number[] { const order = x.map((_, i) => i).sort((a, b) => x[a] - x[b]); const out = x.map(() => 0); let start = 0; while (start < x.length) {
    let end = start + 1;
    while (end < x.length && x[order[end]] === x[order[start]])
        end++;
    for (let j = start; j < end; j++)
        out[order[j]] = (start + 1 + end) / 2;
    start = end;
} return out; }
function quantile(x: number[], p: number): number { const y = [...x].sort((a, b) => a - b), h = (y.length - 1) * p, j = Math.floor(h), f = h - j; return y[j] * (1 - f) + y[Math.min(j + 1, y.length - 1)] * f; }
function compound(x: number[]): number { if (x.some(v => v <= -1))
    fail('INVALID_RETURN'); return Math.expm1(sum(x.map(Math.log1p))); }
/** erfc(|z|/sqrt(2)) via regularized Gamma(1/2,x); converged series/CF. */
function normalP(z: number): number {
    const x = z * z / 2, a = 0.5, lg = 0.5723649429247001;
    if (x === 0)
        return 1;
    const factor = Math.exp(-x + a * Math.log(x) - lg);
    if (x < a + 1) {
        let term = 1 / a, total = term, ap = a;
        for (let i = 1; i < 500; i++) {
            ap++;
            term *= x / ap;
            total += term;
            if (Math.abs(term) < Math.abs(total) * 1e-15)
                break;
        }
        return Math.max(0, 1 - total * factor);
    }
    let b = x + 1 - a, c = 1e300, d = 1 / b, h = d;
    for (let i = 1; i < 500; i++) {
        const an = -i * (i - a);
        b += 2;
        d = an * d + b;
        if (Math.abs(d) < 1e-300)
            d = 1e-300;
        c = b + an / c;
        if (Math.abs(c) < 1e-300)
            c = 1e-300;
        d = 1 / d;
        const delta = d * c;
        h *= delta;
        if (Math.abs(delta - 1) < 1e-15)
            break;
    }
    return Math.max(0, Math.min(1, factor * h));
}
export function ols(y: number[], x: number[][], lags = 0): Result {
    const n = y.length, p = x[0].length;
    same(y, x);
    if (n <= p)
        fail('INSUFFICIENT_DATA');
    integer(lags, 0, n - 1);
    const cols = tr(x), scales = cols.map(c => Math.sqrt(dot(c, c)));
    if (scales.some(s => s === 0))
        fail('SINGULAR_DESIGN');
    const q: number[][] = [], r = Array.from({ length: p }, () => Array(p).fill(0) as number[]);
    for (let j = 0; j < p; j++) {
        let v = cols[j].map(z => z / scales[j]);
        for (let pass = 0; pass < 2; pass++)
            for (let i = 0; i < j; i++) {
                const proj = dot(q[i], v);
                r[i][j] += proj;
                v = v.map((z, t) => z - proj * q[i][t]);
            }
        r[j][j] = Math.sqrt(dot(v, v));
        if (r[j][j] < 1e-10)
            fail('SINGULAR_DESIGN');
        q.push(v.map(z => z / r[j][j]));
    }
    const solve = (v: number[]): number[] => { const b = Array(p).fill(0) as number[]; for (let i = p - 1; i >= 0; i--) {
        let s = 0;
        for (let j = i + 1; j < p; j++)
            s += r[i][j] * b[j];
        b[i] = (v[i] - s) / r[i][i];
    } return b; };
    const beta = solve(q.map(c => dot(c, y))).map((b, i) => b / scales[i]), fitted = x.map(row => dot(row, beta)), residuals = y.map((v, i) => v - fitted[i]);
    const invr = tr(Array.from({ length: p }, (_, j) => solve(Array.from({ length: p }, (_, i) => Number(i === j)))));
    const bread = mm(invr, tr(invr)).map((row, i) => row.map((v, j) => v / scales[i] / scales[j]));
    const scores = x.map((row, t) => row.map(v => v * residuals[t])), meat = mm(tr(scores), scores);
    for (let lag = 1; lag <= lags; lag++) {
        const w = 1 - lag / (lags + 1);
        for (let t = lag; t < n; t++)
            for (let i = 0; i < p; i++)
                for (let j = 0; j < p; j++)
                    meat[i][j] += w * (scores[t][i] * scores[t - lag][j] + scores[t - lag][i] * scores[t][j]);
    }
    const cov = mm(mm(bread, meat), bread), se = cov.map((row, i) => Math.sqrt(Math.max(0, row[i]))), sse = dot(residuals, residuals), ym = mean(y), sst = sum(y.map(v => (v - ym) ** 2));
    return { coefficients: beta, standard_errors: se, fitted, residuals, r_squared: sst === 0 ? null : 1 - sse / sst, n, df_residual: n - p, hac_lags: lags, residual_sum_squares: sse, qr_min_diagonal: Math.min(...r.map((row, i) => row[i])) };
}
function construct(d: Data, op: string): Result {
    if (op === 'composite') {
        required(d, ['features', 'weights', 'directions']);
        const f = mat(d.features, 3), w = vec(d.weights), directions = vec(d.directions);
        same(w, directions, f[0]);
        if (Math.min(...w) < 0 || Math.abs(sum(w) - 1) > 1e-10 || directions.some(v => Math.abs(v) !== 1))
            fail('INVALID_PARAMETER');
        const z = tr(tr(f).map(standard)), components = z.map(row => row.map((v, j) => v * w[j] * directions[j])), out = components.map(sum);
        return { ids: ids(d, f.length), scores: out, components, standardized: z, primary: out[0] };
    }
    required(d, ['scores']);
    const x = vec(d.scores, 2), n = x.length, names = ids(d, n);
    if (op === 'quantile') {
        const count = integer(d.buckets ?? 5, 2, n), order = x.map((_, i) => i).sort((a, b) => x[a] - x[b] || (names[a] < names[b] ? -1 : names[a] > names[b] ? 1 : 0)), buckets = Array(n).fill(0) as number[];
        order.forEach((i, j) => buckets[i] = 1 + Math.floor(j * count / n));
        const counts = Array.from({ length: count }, (_, j) => buckets.filter(b => b === j + 1).length), weights = buckets.map(b => 1 / counts[b - 1]);
        return { ids: names, order: order.map(i => names[i]), buckets, counts, weights, primary: counts[count - 1] };
    }
    if (op === 'sector') {
        required(d, ['sectors']);
        const sectors = d.sectors;
        if (!Array.isArray(sectors))
            fail('INVALID_SHAPE');
        same(x, sectors);
        if (sectors.some((v: unknown) => typeof v !== 'string' || !v))
            fail('INVALID_SECTOR');
        const group: Record<string, number> = Object.create(null);
        for (const g of [...new Set(sectors as string[])].sort())
            group[g] = mean(x.filter((_, i) => sectors[i] === g));
        const out = x.map((v, i) => v - group[sectors[i]]), sums: Record<string, number> = Object.create(null);
        for (const g of Object.keys(group))
            sums[g] = sum(out.filter((_, i) => sectors[i] === g));
        return { ids: names, scores: out, group_means: group, group_sums: sums, primary: Math.max(...Object.values(sums).map(Math.abs)) };
    }
    if (op === 'beta_neutral' || op === 'residual') {
        required(d, [op === 'beta_neutral' ? 'betas' : 'controls']);
        const controls = op === 'beta_neutral' ? vec(d.betas).map(v => [v]) : mat(d.controls);
        same(x, controls);
        const design = controls.map(row => [1, ...row]), fit = ols(x, design, 0), u = fit.residuals as number[], gross = sum(u.map(Math.abs));
        if (op === 'beta_neutral' && gross <= 1e-12 * Math.max(1, sum(x.map(Math.abs))))
            fail('ZERO_RESIDUAL');
        const out = op === 'beta_neutral' ? u.map(v => v / gross) : u, exposures = tr(design).map(col => dot(col, out));
        return { ids: names, scores: out, residuals: u, fitted: fit.fitted, coefficients: fit.coefficients, exposures, gross: sum(out.map(Math.abs)), primary: Math.max(...exposures.map(Math.abs)) };
    }
    const p = num(d.tail ?? 0.05);
    if (p < 0 || p >= 0.5)
        fail('INVALID_PARAMETER');
    const lo = quantile(x, p), hi = quantile(x, 1 - p), clipped = x.map(v => Math.max(lo, Math.min(hi, v))), rank = ranks(clipped), out = rank.map(v => 2 * (v - 1) / (n - 1) - 1);
    return { ids: names, lower: lo, upper: hi, clipped, ranks: rank, scores: out, primary: out[0] };
}
/** D17-F03-A05 public boundary. No mutation, implicit imputation or silent failure. */
export function compute(input: unknown): Result {
    const op = "residual";
    try {
        if (!input || typeof input !== 'object' || Array.isArray(input))
            fail('INVALID_SHAPE');
        const d = input as Data;
        if (Object.values(d).some(v => v === null))
            fail('INVALID_NUMBER');
        context(d, op);
        const result = construct(d, op);
        const check = (v: unknown): void => { if (typeof v === 'number' && !Number.isFinite(v))
            fail('NUMERICAL_FAILURE'); if (Array.isArray(v))
            v.forEach(check);
        else if (v && typeof v === 'object')
            Object.values(v).forEach(check); };
        check(result);
        return { status: 'ok', method: op, ...result };
    }
    catch (error) {
        if (error instanceof ContractError)
            return { status: 'error', method: op, code: error.message };
        throw error;
    }
}